Question

A can do a piece of work in 10 days , and B can do the same work in 20 days . With the help of C , they finished the work in 4 days . C can do the work in how many days, working alone ?

Answer 1

A can do work in $10$ days

$\therefore$ A does $\frac{1}{10}$ of the work in $1$ day

Similarly B does $\frac{1}{20}$ of the work in $1$ day

Let C complete the work in 'x' days C does $\frac{1}{x}$ the work in $1$ day

In $4$ days, A,B & C complete the work

$\Rightarrow 4(\frac{1}{10}+\frac{1}{20}+\frac{1}{x})=1$

$\frac{4}{x}=\frac{2}{5}$

$x=10$